Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA$(p,d,q)$ models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes $N \in \{100, 200, 500, 1000\}$ and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with $N=500$, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and $χ^2(3)$ innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry ($|γ_3| \geq 0.5$) and $N \geq 200$, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typ
We study of millions of scientific, technological, and artistic innovations and find that the innovation gap faced by women is far from universal. No gap exists for conventional innovations. Rather, the gap is pervasively rooted in innovations that combine ideas in unexpected ways - innovations most critical to scientific breakthroughs. Further, at the USPTO we find that female examiners reject up to 33 percent more unconventional innovations by women inventors than do male examiners, suggesting that gender discrimination weakly explains this innovation gap. Instead, new data indicate that a configuration of institutional practices explains the innovation gap. These practices compromise the expertise women examiners need to accurately assess unconventional innovations and then "over-assign" women examiners to women innovators, undermining women's innovations. These institutional impediments negatively impact innovation rates in science but have the virtue of being more amenable to actionable policy changes than does culturally ingrained gender discrimination.
We consider the persistence probabilities of an autoregressive chain of order one with continuous innovations. In the case of positive drifts, we show that these persistence probabilities are compound-geometric and satisfy a Baxter-Spitzer factorization generalizing that of the random walk. In the case of negative drifts, we exhibit a discrete Van Dantzig problem, which implies that the Baxter-Spitzer factorization never happens, except in a degenerate case. For positive drifts and log-concave innovations, we show that the first passage time in $(-\infty,0)$ has a log-convex distribution, whereas in the case of negative drifts and log-convex innovations on ${\mathbb R}^+$, it has a log-concave distribution. The case of the bi-exponential innovations is studied in detail, which leads for positive drifts to an additive factorization of the exponential law.
The rapid rise of AI is poised to disrupt the labor market. However, AI is not a monolith; its impact depends on both the nature of the innovation and the jobs it affects. While computational approaches are emerging, there is no consensus on how to systematically measure an innovation's disruptive potential. Here, we calculate the disruption index of 3,237 U.S. AI patents (2015-2022) and link them to job tasks to distinguish between "consolidating" AI innovations that reinforce existing structures and "disruptive" AI innovations that alter them. Our analysis reveals that consolidating AI primarily targets physical, routine, and solo tasks, common in manufacturing and construction in the Midwest and central states. By contrast, disruptive AI affects unpredictable and mental tasks, particularly in coastal science and technology sectors. Surprisingly, we also find that disruptive AI disproportionately affects areas already facing skilled labor shortages, suggesting disruptive AI technologies may accelerate change where workers are scarce rather than replacing a surplus. Ultimately, consolidating AI appears to extend current automation trends, while disruptive AI is set to transform co
Business innovations are often arising from new combinations of pre-existing systems into new ones, coherently assembling features from their sources. We propose an abstract mathematical concept from category theory, the presheaf, to efficiently represent such coherent feature combinations. Moreover, operations on presheaves will allow us to formally describe and analyze business innovations that arise from novel mergings of systems from different domains. Equipped with such tools we provide an example by analyzing a successful case of such type of recombinant innovation, the digital hub concept proposed by Steve Jobs. The example shows how our framework can be used to bring formal rigor while preserving a fundamentally qualitative reasoning style.
Rogers' diffusion of innovations theory asserts that cultural similarity among individuals plays a crucial role in the acceptance of an innovation in a community. However, most studies on the diffusion of innovations have relied on epidemic-like models where the individuals have no preference on whom they interact with. Here, we use an agent-based model to study the diffusion of innovations in a community of synthetic heterogeneous agents whose interaction preferences depend on their cultural similarity. The community heterogeneity and the agents' interaction preferences are described by Axelrod's model, whereas the diffusion of innovations is described by a variant of the Daley and Kendall model of rumour propagation. The interplay between the social dynamics and the spreading of the innovation is controlled by the parameter $p \in [0,1]$, which yields the probability that the agent engages in social interaction or attempts to spread the innovation. Our findings support Roger's empirical observations that cultural heterogeneity curbs the diffusion of innovations.
The world has witnessed rapid technological transformation, past couple of decades and with Advent of Cloud computing the landscape evolved exponentially leading to efficient and scalable application development. Now, the past couple of years the digital ecosystem has brought in numerous innovations with integration of Artificial Intelligence commonly known as AI. This paper explores how AI and cloud computing intersect to deliver transformative capabilities for modernizing applications by providing services and infrastructure. Harnessing the combined potential of both AI & Cloud technologies, technology providers can now exploit intelligent resource management, predictive analytics, automated deployment & scaling with enhanced security leading to offering innovative solutions to their customers. Furthermore, by leveraging such technologies of cloud & AI businesses can reap rich rewards in the form of reducing operational costs and improving service delivery. This paper further addresses challenges associated such as data privacy concerns and how it can be mitigated with robust AI governance frameworks.
The diffusion of innovations theory has been studied for years. Previous research efforts mainly focus on key elements, adopter categories, and the process of innovation diffusion. However, most of them only consider single innovations. With the development of modern technology, recurrent innovations gradually come into vogue. In order to reveal the characteristics of recurrent innovations, we present the first large-scale analysis of the adoption of recurrent innovations in the context of mobile app updates. Our analysis reveals the adoption behavior and new adopter categories of recurrent innovations as well as the features that have impact on the process of adoption.
We consider a stationary linear $AR(p)$ model with zero mean. The autoregression parameters as well as the distribution function (d.f.) $G(x)$ of innovations are unknown. We consider two situations. In the first situation the observations are a sample from a stationary solution of $AR(p)$. Interesting and essential problem is to test symmetry of $G(x)$ with respect to zero. If hypothesis of symmetry is valid then it is possible to construct nonparametric estimators of $AR(p)$ parameters, for example, GM-estimators, minimum distance estimators and others. First of all we estimate unknown parameters of autoregression and find residuals. Based on them we construct a kind of empirical d.f., which is a counterpart of empirical d.f of the unobservable innovations. Our test statistic is the functional of omega-square type from this residual empirical d.f. Its asymptotic d.f. under the hypothesis and the local alternatives are found. In the second situation the observations subject to gross errors (outliers). The distribution of outliers is unknown, their intensity is $O(n^{-1/2})$, $n$ is the sample size. We test the symmetry of innovations again but by constructing the Pearson's type sta
An innovations sequence of a time series is a sequence of independent and identically distributed random variables with which the original time series has a causal representation. The innovation at a time is statistically independent of the history of the time series. As such, it represents the new information contained at present but not in the past. Because of its simple probability structure, an innovations sequence is the most efficient signature of the original. Unlike the principle or independent component analysis representations, an innovations sequence preserves not only the complete statistical properties but also the temporal order of the original time series. An long-standing open problem is to find a computationally tractable way to extract an innovations sequence of non-Gaussian processes. This paper presents a deep learning approach, referred to as Innovations Autoencoder (IAE), that extracts innovations sequences using a causal convolutional neural network. An application of IAE to the one-class anomalous sequence detection problem with unknown anomaly and anomaly-free models is also presented.
The great influence of Bitcoin has promoted the rapid development of blockchain-based digital currencies, especially the altcoins, since 2013. However, most altcoins share similar source codes, resulting in concerns about code innovations. In this paper, an empirical study on existing altcoins is carried out to offer a thorough understanding of various aspects associated with altcoin innovations. Firstly, we construct the dataset of altcoins, including source code repositories, GitHub fork relations, and market capitalizations (cap). Then, we analyze the altcoin innovations from the perspective of source code similarities. The results demonstrate that more than 85% of altcoin repositories present high code similarities. Next, a temporal clustering algorithm is proposed to mine the inheritance relationship among various altcoins. The family pedigrees of altcoin are constructed, in which the altcoin presents similar evolution features as biology, such as power-law in family size, variety in family evolution, etc. Finally, we investigate the correlation between code innovations and market capitalization. Although we fail to predict the price of altcoins based on their code similaritie
Competition is one of the most fundamental phenomena in physics, biology and economics. Recent studies of the competition between innovations have highlighted the influence of switching costs and interaction networks, but the problem is still puzzling. We introduce a model that reveals a novel multi-percolation process, which governs the struggle of innovations trying to penetrate a market. We find that innovations thrive as long as they percolate in a population, and one becomes dominant when it is the only one that percolates. Besides offering a theoretical framework to understand the diffusion of competing innovations in social networks, our results are also relevant to model other problems such as opinion formation, political polarization, survival of languages and the spread of health behavior.
We study the introduction of lexical innovations into a community of language users. Lexical innovations, i.e., new terms added to people's vocabulary, play an important role in the process of language evolution. Nowadays, information is spread through a variety of networks, including, among others, online and offline social networks and the World Wide Web. The entire system, comprising networks of different nature, can be represented as a multi-layer network. In this context, lexical innovations diffusion occurs in a peculiar fashion. In particular, a lexical innovation can undergo three different processes: its original meaning is accepted; its meaning can be changed or misunderstood (e.g., when not properly explained), hence more than one meaning can emerge in the population; lastly, in the case of a loan word, it can be translated into the population language (i.e., defining a new lexical innovation or using a synonym) or into a dialect spoken by part of the population. Therefore, lexical innovations cannot be considered simply as information. We develop a model for analyzing this scenario using a multi-layer network comprising a social network and a media network. The latter r
Performances of building energy innovations are most of the time dependent on the external climate conditions. This means a high performance of a specific innovation in a certain part of Europe, does not imply the same performances in other regions. The mapping of simulated building performances at the EU scale could prevent the waste of potential good ideas by identifying the best region for a specific innovation. This paper presents a methodology for obtaining maps of performances of building innovations that are virtually spread over whole Europe. It is concluded that these maps are useful for finding regions at the EU where innovations have the highest expected performances.
Gender representation in the physical sciences remains inequitable and continues to lag behind other fields. Even though there exists adequate documentation regarding programmatic postures and innovations, difficulties persist within the physics discipline. In this paper, we present innovative, programmatic implementations over an eight-year period at an undergraduate, liberal arts physics program. Some of these innovations accord with nationally-published, `best practices' for undergraduate physics programs, while others are novel to the program's context. Within this eight-year period, alterations are separated into curricular, co-curricular, and experiential elements. Innovations are introduced in some detail, and data are presented before, during, and after their introduction. While it is currently impossible to say which elements had the greatest impact, the synergistic combination did have a positive effect on the program. Not only did the number of total majors and graduates increase, there was a 200% increase of women degree recipients compared to the previous ten years, which boosted average graduation rates above the national average (30% > 20%). Women were retained wi
The paper provides simple formulas of Bayesian filtering for the exact recursive computation of state conditional probability density functions given quantized innovations signal measurements of a linear stochastic system. This is a topic of current interest because the innovations signal should be white and therefore efficient in its use of channel capacity and in the design and optimization of the quantizer. Earlier approaches, which we reexamine and characterize here, have relied on assumptions concerning densities or approximations to yield recursive solutions, which include the sign-of-innovations Kalman filter and a Particle filtering technique. Our approach uses the Kalman filter innovations at the transmitter side and provides a point of comparison for the other methods, since it is based on the Bayesian filter. Computational examples are provided.
A number of determinants predict the adoption of Information Systems (IS) security innovations. Amongst, perceived vulnerability of IS security threats has been examined in a number of past explorations. In this research, we examined the processes pursued in analysing the relationship between perceived vulnerability of IS security threats and the adoption of IS security innovations. The study uses Systematic Literature Review (SLR) method to evaluate the practice involved in examining perceived vulnerability on IS security innovation adoption. The SLR findings revealed the appropriateness of the existing empirical investigations of the relationship between perceived vulnerability of IS security threats on IS security innovation adoption. Furthermore, the SLR results confirmed that individuals who perceives vulnerable to an IS security threat are more likely to engage in the adoption an IS security innovation. In addition, the study validates the past studies on the relationship between perceived vulnerability and IS security innovation adoption.
Algorithmic innovation in the pretraining of large language models has driven a massive reduction in the total compute required to reach a given level of capability. In this paper we empirically investigate the compute requirements for developing algorithmic innovations. We catalog 36 pre-training algorithmic innovations used in Llama 3 and DeepSeek-V3. For each innovation we estimate both the total FLOP used in development and the FLOP/s of the hardware utilized. Innovations using significant resources double in their requirements each year. We then use this dataset to investigate the effect of compute caps on innovation. Our analysis suggests that compute caps alone are unlikely to dramatically slow AI algorithmic progress. Even stringent compute caps -- such as capping total operations to the compute used to train GPT-2 or capping hardware capacity to 8 H100 GPUs -- could still have allowed for half of the cataloged innovations.
This paper analyses how firms' skill development strategies affect their propensity to introduce innovation. We develop an adjustment-cost framework that links human capital theory and institutionalist and evolutionary approaches, considering innovation as an activity that entails costs in labour adjustment arising either from the training activities of workers or the recruitment of skilled employees. Using a two-wave panel of Italian manufacturing firms observed in 2017-2018 and 2019-2020, we analyse firms' adoption of total, product, process, and circular innovation as a function of internal training practices and of external skills acquisition. Overall, the empirical analysis confirms the expected positive relationship between training and innovation, while also revealing important nuances in the workforce upskilling strategies required for different types of innovation. Moreover, while training activities and skills development are essential across all forms of innovation, our findings indicate that internal training is particularly effective in supporting the implementation of circular innovations. By contrast, external recruitment appears to be consistently necessary whenever
British biophysics has a tradition of scientific invention and innovation, resulting in new technologies transforming biological insight, such as rapid DNA sequencing, super-resolution and label-free microscopy, high-throughput and single-molecule bio-sensing, and bio-inspired synthetic materials. Some advances were established through democratised platforms and many have biomedical success, a key example involving the SARS-CoV-2 spike protein during the COVID-19 pandemic. Here, three UK labs made crucial contributions revealing how the spike protein targets human cells, and how therapies of vaccines and neutralizing nanobodies work, enabled largely through biophysical innovations of cryo-electron microscopy. Here, we discuss leading-edge innovations which resulted from discovery-led British 'Physics of Life' research (capturing blends of physical-life sciences research in the UK including biophysics and biological physics) and have matured into wide-reaching sustainable commercial ventures enabling translational impact. We describe the biophysical science which led to these academic spinouts, presenting the scientific questions that were addressed through innovating new techniques